[Paper Review] Transient degrees of freedom and stability

Varda F. Hagh, Sidney R. Nagel+3 more|arXiv (Cornell University)|May 23, 2021

Mechanical and Optical Resonators4 citations

TL;DR

This paper introduces numerical protocols that transiently manipulate degrees of freedom—such as particle sizes or stiffnesses—to create exceptionally stable jammed packings in amorphous solids. By first introducing and then removing these degrees of freedom, the method drives systems into deeper energy minima with suppressed low-frequency quasilocalized modes, with particle size variations proving more effective than stiffness tuning at enhancing mechanical stability.

ABSTRACT

The mechanical stability of a physical system plays a crucial role in determining its excitations and response to strain. Recent advances have led to protocols that can create particularly stable amorphous solids. Such systems, whether they be physical systems created using vapor-deposition or numerical model systems created using swap or breathing algorithms, exist in exceptionally deep energy minima marked by the absence of low-frequency quasilocalized modes. We introduce new numerical protocols for creating stable jammed packings that first introduce and subsequently remove degrees of freedom such as particle sizes or particle stiffnesses. We find that different choices for the degrees of freedom can lead to very different results. For jammed packings, degrees of freedom that couple to the jamming transition, e.g., particle sizes, push the system to much more stable and deeper energy minima than those that only couple to interaction stiffnesses.

Motivation & Objective

• To develop numerical protocols that enhance mechanical stability in amorphous solids by transiently introducing and removing degrees of freedom.
• To investigate how different types of degrees of freedom—such as particle sizes or stiffnesses—affect the stability of jammed packings.
• To identify which degrees of freedom most effectively suppress low-frequency quasilocalized modes and deepen energy minima.
• To compare the effectiveness of particle size variations versus stiffness tuning in achieving stable, low-energy configurations.

Proposed method

• The method introduces temporary degrees of freedom, such as variable particle sizes or stiffnesses, during the protocol to explore a broader configuration space.
• It employs numerical algorithms that first expand the system's degrees of freedom to access deeper energy minima.
• After reaching a stable configuration in the extended space, the degrees of freedom are gradually removed to return to the original system parameters.
• The protocol uses the jamming transition as a guide, favoring degrees of freedom that couple directly to it, such as particle size.
• The stability is assessed by analyzing the energy landscape and the presence of low-frequency quasilocalized modes.
• The approach is tested on model systems using protocols analogous to vapor deposition or swap algorithms.

Experimental results

Research questions

• RQ1 How do transient degrees of freedom influence the depth of energy minima in jammed amorphous packings?
• RQ2 Which types of degrees of freedom—particle size or stiffness—lead to greater mechanical stability in amorphous solids?
• RQ3 To what extent do degrees of freedom coupled to the jamming transition enhance system stability compared to those only affecting interaction stiffness?
• RQ4 Can the removal of transient degrees of freedom preserve the enhanced stability of the final configuration?
• RQ5 What is the role of low-frequency quasilocalized modes in determining the mechanical response of the final jammed state?

Key findings

• Particle size variations as transient degrees of freedom lead to significantly deeper energy minima compared to stiffness tuning.
• Systems stabilized via particle size manipulation exhibit a marked suppression of low-frequency quasilocalized modes.
• Degrees of freedom coupled to the jamming transition, such as particle sizes, are more effective at enhancing stability than those only affecting interaction stiffness.
• The protocol successfully generates jammed packings with enhanced mechanical stability by leveraging transient degrees of freedom.
• The final configurations retain high stability even after the removal of transient degrees of freedom, indicating robust energy landscape optimization.